How do you find the center and radius of a circle using a polynomial #x^2 + y^2 - 6x + 10y + 9 = 0#?

1 Answer
May 24, 2018

Answer:

Center is at # (3 , -5)# and radius is # r=5 # unit.

Explanation:

#x^2+y^2-6 x +10 y +9 =0# or

#(x^2 -6 x) +(y^2+10 y )= -9 # or

#(x^2 -6 x +9) +(y^2+10 y +25 )=34 -9 # or

#(x-3)^2 +(y +5)^2=5^2 #. The center-radius form of the circle

equation is #(x – h)^2 + (y – k)^2 = r^2#, with the center being at

the point #(h, k)# and the radius being #r#. Center is at

# (3 , -5)# and radius is # r=5 # unit.

graph{x^2+y^2-6 x+10 y+9=0 [-20, 20, -10, 10]} [Ans]